The main theorem of this paper complements the tame-wild dichotomy for commutative Noetherian rings, obtained by Klingler and Levy [14]–[16]. They gave a complete classification of all finitely generated modules over Dedekind-like rings (cf. Definition 1.1) and showed that, over any ring that is not a homomorphic image of a Dedekind-like ring, the category of finite-length modules has wild repr...

Let KV ] G be the invariant ring of a nite linear group G GL(V), and let GU be the pointwise stabilizer of a subspace U V. We prove that the following numbers associated to the invariant ring decrease if one passes from KV ] G to KV ] G U : the minimal number of homogeneous generators, the maximal degree of the generators, the number of syzygies and other Betti numbers, the complete intersectio...

Let K[V ] be the invariant ring of a finite linear group G ≤ GL(V ), and let GU be the pointwise stabilizer of a subspace U ≤ V . We prove that the following numbers associated to the invariant ring do not increase if one passes from K[V ] to K[V ]U : the minimal number of homogeneous generators, the maximal degree of the generators, the number of syzygies and other Betti numbers, the complete ...

Let [Formula: see text] be a simple undirected graph. The family of all matchings forms simplicial complex called the matching text]. Here, we give classification graphs with Gorenstein complex. Also study when is Cohen–Macaulay and, in certain classes graphs, fully characterize those which have In particular, graph girth at least five or complete Cohen–Macaulay.

R.G. and Perez proved that under certain conditions the test ideal of a module closure agrees with trace closure. We use this fact to compute ideals various rings respect closures coming from their indecomposable maximal Cohen–Macaulay modules. also give an easier way hypersurface ring in three variables particular type matrix factorization.

We study Stanley decompositions and show that Stanley’s conjecture on Stanley decompositions implies his conjecture on partitionable Cohen-Macaulay simplicial complexes. We also prove these conjectures for all Cohen-Macaulay monomial ideals of codimension 2 and all Gorenstein monomial ideals of codimension 3.

In this thesis we discuss a moduli space of projective curves with a map to a given projective space P. The functor CM parametrizes curves, that is, Cohen-Macaulay schemes of pure dimension 1, together with a finite map to P that is an isomorphism onto its image away from a finite set of closed points. We proof that CM is an algebraic space by contructing a scheme W and a representable, surject...

Let (R,m) be a local ring, I a proper ideal of R and M a finitely generated R-module of dimension d. We discuss the local homology modules of H I (M). When M is Cohen-Macaulay, it is proved that H d m(M) is co-CohenMacaulay of N.dimension d and H x d (H m(M)) = M̂ where x = (x1, . . . , xd) is a system of parameters for M . 2000 Mathematics Subject Classification: 13C14, 13D45